Is there a name for that form of joke, where you perceive a word inside another word?
The particular observation in the post title was made by Meade, reading about the son of a widow who hoped for succession rights to a rent-stabilized apartment.
ADDED: TV Tropes has a page titled "You Put the X in XY," which includes examples that are mostly really dumb, like "You put the itch in bitch."
The Kindle search tool is good (too good) at exposing these words within words because its search tool won't let you restrict the search to an actual word. For example, you'll have a hell of a time looking for a word like "hat," which appears in every "what" and "that." But I've made some delightful discoveries by accident this way.